Childrens Encoding and Solving of Mathematical Equations

Noelle M. Crooks, University of Wisconsin - Madison

Martha W. Alibali, University of Wisconsin - Madison

Abstract

Elementary school children often fail to correctly solve
equivalence problems (e.g., 3+4+5=3+__). This study investigated whether
childrens difficulties are due, in part, to incorrectly encoding
(internally representing) the equivalence problems and tested whether
improvements in encoding would lead to improvements in problem solving. To
address these issues, we developed a new measure of problem encoding that used a
change detection paradigm, and we also utilized more traditional reconstruction
and recognition measures. Children completed measures of encoding and problem
solving before and after a brief lesson designed to improve their encoding.
Change detection performance was significantly correlated with performance on the
traditional encoding measures. Moreover, all three encoding measures were related
to childrens pretest problem-solving performance. Finally, pre- to posttest
changes in childrens encoding appeared to be related to changes in
childrens problem-solving performance. These findings suggest that
improving problem encoding should be a target of instruction about equations.